Research To understand protein's function and to design new proteins with new functions, it is essential to know the physical principles that control the structure, folding, stability, and dynamics of protein molecules. Our long-term research interest is to investigate these principles and use them to solve practical problems in basic medical research and development of protein drugs. Currently, we are studying the mechanism of protein folding and learning to design proteins by phage-display. The Mechanism of Protein Folding In the past several years, we focused on studying the folding mechanism of small proteins including cytochrome c (104 amino acids), Rd-apocyt b562 (106 amino acids), and barnase (110 amino acids). These small proteins fold kinetically in an apparent two-state manner. However, we found that they have partially folded hidden intermediates after the rate-limiting transition states. These results were demonstrated using various experimental tools including native-state hydrogen exchange and stopped-flow fluorescence. Moreover, using a hydrogen exchange-directed protein engineering approach, we are able to populate the partially unfolded intermediate of Rd-apocyt b562 and determined its high-resolution structure. This is the first high-resolution structure of a folding intermediate. To our surprise, significant non-native hydrophobic interactions were found in the partially unfolded structure. These results contradict the so called "New View" of protein folding that hypothesizes that small proteins fold through multiple pathways without going through intermediate states but provide strong evidence for the earlier hypothesis that intermediates are important for solving the large-scale conformation search problem: the Levinthal paradox. We have also developed a theoretical model to explain why different small proteins (< 120 amino acids) fold with different rates, which span six orders of magnitude from microseconds to seconds. We found that the size (number of folded residues) of the transition state is dominantly controlled by the topological complexity of the native structure and correlates with the folding rate. Protein Design by Phage Display In addition to the protein folding studies, we also used a phage-display and proteolysis to design stably folded proteins. In this method, the design procedure involves following steps: (1) rational design of target fold; (2) generation of multiple mutations in the core of the target protein; (3) display the mutants on the surface of the phages; and (4) selection for stably folded proteins by challenging the protein library with proteases. Using this approach, we have successfully converted a partially unfolded apocytochrome b562 to a fully folded four-helix bundle protein. However, the consensus sequence for the selected proteins has hydrophilic residues at the positions that are designed to have hydrophobic residues. Recently, we have determined the high-resolution structure of one of the selected protein by NMR: Rd-apocyt b562. It was found that the new hydrophobic core was constituted with the hydrophobic residues that are neighbors of the mutated residues. These results support the hydrophobic core-directed protein design strategy but also indicate that detailed structures for the selected proteins are difficult to predict.